Embodiments of the invention relate generally to diagnostic imaging and, more particularly, to a system and method of iterative image reconstruction for computed tomography.
Typically, in computed tomography (CT) imaging systems, an x-ray source emits a fan-shaped beam toward a subject or object, such as a patient or a piece of luggage. Hereinafter, the terms “subject” and “object” shall include anything capable of being imaged. The beam, after being attenuated by the subject, impinges upon an array of radiation detectors. The intensity of the attenuated beam radiation received at the detector array is typically dependent upon the attenuation of the x-ray beam by the subject. Each detector element of the detector array produces a separate electrical signal indicative of the attenuated beam received by each detector element. The electrical signals are transmitted to a data processing system for analysis which ultimately produces an image.
Generally, the x-ray source and the detector array are rotated about the gantry within an imaging plane and around the subject. X-ray sources typically include x-ray tubes, which emit the x-ray beam at a focal point. X-ray detectors typically include a collimator for collimating x-ray beams received at the detector, a scintillator for converting x-rays to light energy adjacent the collimator, and photodiodes for receiving the light energy from the adjacent scintillator and producing electrical signals therefrom.
Typically, each scintillator of a scintillator array converts x-rays to light energy. Each scintillator discharges light energy to a photodiode adjacent thereto. Each photodiode detects the light energy and generates a corresponding electrical signal. The outputs of the photodiodes are then transmitted to the data processing system for image reconstruction. Alternatively, x-ray detectors may use a direct conversion detector, such as a CZT detector, in lieu of a scintillator.
CT systems typically use analytical algorithms such as a filtered back-projection algorithm to reconstruct images from the acquired image data. Alternatively, an iterative technique may be used for reconstruction to improve image quality. For example, a model-based iterative reconstruction algorithm may be used to estimate an image based on pre-determined models of the CT system, the acquired projection data, and the reconstructed image such that the reconstructed image best fits the image data.
A typical model-based iterative reconstruction framework reconstructs an image of the scanned object from projection data according to the general equation:
                                          x            ^                    =                      arg            ⁢                                          min                                  x                  ∈                  Ω                                            ⁢                              {                                                      D                    ⁡                                          (                                              y                        -                                                  F                          ⁡                                                      (                            x                            )                                                                                              )                                                        +                                      U                    ⁡                                          (                      x                      )                                                                      }                                                    ,                            (                  Eqn          .                                          ⁢          1                )            where x is the discrete vector of reconstructed values (for instance a 3D image), y is the discrete vector of measurement values (e.g., a CT projection dataset), Ω is a constraint set for the space of solutions (e.g., the set of non-negative solutions in x), D(·) is an convex scalar valued function (e.g., a log-likelihood function used as a metric for relating the measurement vector y to the reconstructed vector x), U(·) is a scalar value regularization term (e.g., a function that penalizes local differences between voxel elements in x), and F(·) is a transformation of the image space x in a manner similar to the scanning system (e.g., a CT scanner).
An iterative optimization algorithm is used to solve Eqn. 1. The quantity F(x) may be modeled as a discretized linear relationship of the form F(x)=Ax, where A is the system matrix for the forward projection of x according to the imaging system. The negative log-likelihood function D(·) is derived from the Poisson distribution of the measurements y via a Taylor series expansion to arrive at a quadratic component of the overall regularized cost function or Maximum A Posteriori (MAP) estimation:
                                          x            ^                    =                      arg            ⁢                                          min                                  x                  ≥                  0                                            ⁢                              {                                                                            1                      2                                        ⁢                                          (                                              y                        -                        Ax                                            )                                        ⁢                                          W                      ⁡                                              (                                                  y                          -                          Ax                                                )                                                                              +                                      U                    ⁡                                          (                      x                      )                                                                      }                                                    ,                            (                  Eqn          .                                          ⁢          2                )            where W is a diagonal conventional statistical weighting matrix whose elements are approximately inversely proportional to the variance in the projection measurements y over the range of weights within the matrix.
The elements of the conventional statistical weighting matrix W are used to control the influence of each individual projection ray during the iterative image reconstruction. Statistical weighting plays a large factor in the quality of the reconstructed results and defines ones of the unique properties of model-based iterative reconstruction relative to standard analytical reconstruction methods such as filtered back-projection.
Conventional statistical weights are calculated from the inverse variance in the actual projection data. In the absence of electronic noise, the inverse variance in projection measurements is calculated to be proportional to the photon count λ:
                                          w            i                    ∝                      1                          σ                              y                i                            2                                      ,                            (                  Eqn          .                                          ⁢          3                )            where y is the projection data. The value a may be calculated using the raw photon count measurements X alone or in combination with the known electronic noise in the data acquisition system.
While conventional statistical weighting techniques such as those described above may be used to reduce image noise, the coefficients used in these standard models are highly spatially-variant for reconstructing complex objects. The resulting large dynamic range in the weights can slow down the convergence of the iterative optimization algorithm and be associated with image artifacts. For instance, in the case of a data inconsistency between the model used for reconstruction and the real projection data, such as when the scanned object moves during the scan and the model assumes no motion is present, large local changes in the conventional statistical weights may increase the magnitude of image artifacts.
Statistical weights are also associated with image texture by controlling the correlation in the noise of the reconstructed image pixels. For medical imaging in particular, image texture is an important consideration when attempting to represent tissue as realistically as possible.
Therefore, it would be desirable to design a system and method of iterative image reconstruction that overcomes the aforementioned drawbacks of conventional statistical weighting techniques.